CF1677A Tokitsukaze and Strange Inequality

Tokitsukaze has a permutation $ p $ of length $ n $ . Recall that a permutation $ p $ of length $ n $ is a sequence $ p_1, p_2, \ldots, p_n $ consisting of $ n $ distinct integers, each of which from $ 1 $ to $ n $ ( $ 1 \leq p_i \leq n $ ). She wants to know how many different indices tuples $ [a,b,c,d] $ ( $ 1 \leq a < b < c < d \leq n $ ) in this permutation satisfy the following two inequalities: $ p_a < p_c $ and $ p_b > p_d $ . Note that two tuples $ [a_1,b_1,c_1,d_1] $ and $ [a_2,b_2,c_2,d_2] $ are considered to be different if $ a_1 \ne a_2 $ or $ b_1 \ne b_2 $ or $ c_1 \ne c_2 $ or $ d_1 \ne d_2 $ .

The first line contains one integer $ t $ ( $ 1 \leq t \leq 1000 $ ) — the number of test cases. Each test case consists of two lines. The first line contains a single integer $ n $ ( $ 4 \leq n \leq 5000 $ ) — the length of permutation $ p $ . The second line contains $ n $ integers $ p_1, p_2, \ldots, p_n $ ( $ 1 \leq p_i \leq n $ ) — the permutation $ p $ . It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 5000 $ .

For each test case, print a single integer — the number of different $ [a,b,c,d] $ tuples.

In the first test case, there are $ 3 $ different $ [a,b,c,d] $ tuples. $ p_1 = 5 $ , $ p_2 = 3 $ , $ p_3 = 6 $ , $ p_4 = 1 $ , where $ p_1 < p_3 $ and $ p_2 > p_4 $ satisfies the inequality, so one of $ [a,b,c,d] $ tuples is $ [1,2,3,4] $ . Similarly, other two tuples are $ [1,2,3,6] $ , $ [2,3,5,6] $ .